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Home  >>  CBSE XII  >>  Math  >>  Matrices
+1 vote

If $A=\begin{bmatrix}2 & 3\\5 & -2\end{bmatrix}$ then express $A^{-1}$ in terms of $A$

$\begin{array}{1 1} \frac{-1}{19} A \\\frac{1}{11} A \\ \frac{1}{19}A \\ -19 \end{array}$

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1 Answer

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  • $A^{-1}=\large\frac{1}{|A|}$$. (Adj \:A)$
$A=\begin{bmatrix}2 & 3\\5 & -2\end{bmatrix}$
$|A|=-4-15=-19$
$Adj\:A=\begin{bmatrix}-2 & -3\\-5 & 2\end{bmatrix}=-\begin{bmatrix}2 & 3\\5 &- 2\end{bmatrix}=-A$
$A^{-1}=\large\frac{1}{|A|}$$. (Adj \:A)$
$\Rightarrow\:A^{-1}=-\large\frac{1}{19}$$\begin{bmatrix}-2 & -3\\-5 & 2\end{bmatrix}$
$=\large\frac{1}{19}$$A$
answered Jan 30, 2014 by rvidyagovindarajan_1
edited Jan 30, 2014 by rvidyagovindarajan_1
 

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